Structure monitoring

ABSTRACT

A method and apparatus for monitoring a structure using an optical fiber based distributed acoustic sensor (DAS) extending along the length of the structure. The DAS is able to resolve a separate acoustic signal with a spatial resolution of 1 m along the length of the fibre, and hence is able to operate with an acoustic positioning system to determine the position of the riser with the same spatial resolution. In addition, the fiber can at the same time also detect much lower frequency mechanical vibrations in the riser, for example such as resonant mode vibrations induced by movement in the surrounding medium. By using vibration detection in combination with acoustic positioning then overall structure shape monitoring can be undertaken, which is useful for vortex induced vibration (VIV) visualisation, fatigue analysis, and a variety of other advanced purposes. The structure may be a sub-sea riser.

TECHNICAL FIELD

The present invention relates to the monitoring of structures such as,for example, sub-sea risers, and particularly to a method and apparatusfor monitoring structures using an optical fiber distributed acousticsensor (DAS) capable of detecting sound at short intervals along thelength of the structure. In one embodiment the DAS system is employed aspart of an acoustic positioning system to help determine the shape ofthe structure along its length. In another embodiment the DAS system isemployed to monitor mechanical vibration of the structure itself. In apreferred embodiment both vibration monitoring and acoustic positioningare undertaken by the same DAS equipment.

BACKGROUND TO THE INVENTION AND PRIOR ART

Sub-sea risers are used to transport materials between the seafloor andthe surface (and vice versa), and are used extensively in the oil andgas industries. They come in several different variants, and are usedfor many purposes, particularly the transport of produced hydrocarbons,as well as production materials, such as injection fluids, controlfluids and gas lift. Risers may be rigid or flexible, and variantsinclude attached risers, pull tube risers, steel catenary risers,top-tensioned risers, riser towers and flexible riser configurations, aswell as drilling risers.

Chevron originally proposed the concept of tracking strategic points ona riser, mooring lines, or other dynamic subsea structures via activehydro-acoustics in the 1990's (Kutlik, R., & Allen, J. (1998). FlowAssurance Instrumentation. Offshore Technology Conference, 8733-MS).However, the length of many risers means that for proper tracking manyindividual hydrophones are required along the length of the riser, whichheretofore has been prohibitively expensive.

In addition to the above, acoustic positioning systems are also known inthe art. One known type of acoustic positioning system is known as a“long-baseline” system. Here, acoustic sources of known location emitcharacteristic sonar pings, usually in response to a ping received froma device the location of which is to be determined. The sonar on thedevice detects the pings, and based on the time elapsed between its ownping and receiving the ping from the known source in reply, togetherwith measurements of the speed of sound given present water conditions,the device is able to calculate its distance from the source. Bycalculating the distance to several different known sources andtriangulating the results, the position of the device relative to theknown positions of the sources can be determined. The technique issubstantially identical to that used in GPS systems. To determinerelative location in 3 dimensions, distance to at least four knownsources is required.

Thus, both acoustic positioning and the concept of the monitoring ofsubsea risers using active hydro acoustics are known in theory, butheretofore no successful deployment of such a system has taken place. Asnoted above, the number of hydrophones required to properly monitor asubsea riser has been prohibitive, and there are challenging deploymentissues.

WO 2012/018460 describes how a distributed optical acoustic sensor canbe used in combination with acoustic pingers that are part of a surveyspread for positioning of one or more objects of interest in relation toa structure carrying the distributed optical acoustic sensor. Suchobjects may include a streamer towed through a body of water, or aseabed cable positioned on the sea floor. Alternatively marine vessels,or fish or marine mammals may also be positioned.

In addition, the applicant's earlier application WO 2010/136810describes an application of a distributed optical acoustic sensor todynamic positioning of a riser. Here an optical fibre sensor measuresthe time of flight of acoustic signals received at different locationsalong the riser, and thereby determines the position of the riser.

Therefore, whilst positioning per se using optical fibre acousticsensors has been suggested in the prior art, there is still no solutionwhich allows for proper monitoring of a riser or other structure alongits whole length, and which particularly allows for fatigue analysis,for example, to take place.

SUMMARY OF THE INVENTION

The present invention addresses the above noted deficiencies of theprior art by providing a method and apparatus for monitoring a structuresuch as a subsea riser using an optical fiber based distributed acousticsensor (DAS) extending along the length of the structure. The DAS isable to resolve a separate acoustic signal with a spatial resolution of1 m along the length of the fibre, and hence is able to operate with anacoustic positioning system to determine the shape of the structure withthe same spatial resolution. In addition, the fiber can at the same timealso detect much lower frequency mechanical vibrations in the structure,for example such as resonant mode vibrations induced by movement in thesurrounding medium. By using vibration detection in combination withacoustic positioning then overall structure shape monitoring can beundertaken, which is useful for vortex induced vibration (VIV)visualisation, fatigue analysis, and a variety of other advancedpurposes.

In view of the above, from one aspect an embodiment of the inventionprovides a method of monitoring the position of a structure using anoptical fiber distributed acoustic sensor deployed in a knownrelationship with respect to the structure such that a known part of theoptical fiber corresponds to a known part of the structure. The methodmay comprise using the optical fiber as a distributed acoustic sensor todetect, at a plurality of acoustic sensor positions along the fibre,acoustic signals emitted by a plurality of acoustic sources deployed atknown positions in an area in which the structure to be monitored islocated. Relative positions of a plurality of the acoustic sensors withrespect to the acoustic sources are then calculated in dependence on thedetected acoustic signals from the acoustic sources. From the calculatedpositions of the sensors along the fibre, a shape, or shape andposition, of the structure can then be determined in further dependenceon the known relationship between the fiber and the structure.

With the above the shape and position of a structure such as a sub-seariser can be monitored in a convenient manner. In this respect, sub searisers often have fiber optic cables passing through them, which may beused as the fiber optic cable of the DAS system. Moreover, such fiberoptic DAS systems can resolve acoustic signals with a spatial resolutionof better than 1 m, and hence high spatial resolution monitoring of thestructure position and movement can be obtained. This allows foradvanced fatigue monitoring and logging, and other such analysis, totake place.

In a preferred embodiment determining the shape, or shape and position,of the structure is repeatedly performed so as to track changes in shapeand/or movement of the structure with respect to time. As noted above,this allows for further monitoring and/or analysis of the structure,such as fatigue monitoring, to be undertaken in dependence on thetracked changes in shape and/or movement of the structure.

In one embodiment the relative position of one of the acoustic sensorson the fiber is determined in dependence upon the relative positiondetermined for one or more others of the sensors. Hence, a prioriknowledge of the fact that the acoustic sensors are positioned along anoptical fiber in a known relationship can be used to improve thepositioning (and hence shape) that is calculated. Specifically, in oneembodiment the relative position found for one of the acoustic sensorson the fiber is checked to determine whether it is within an allowabledistance of the position previously found for another of the acousticsensors on the fibre, given the known length of fiber between therespective positions of the two acoustic sensors on the fiber. If thecalculated position is not within the allowable distance, then one orother of the positions is incorrect, and should be recalculated.

In some embodiments the relative position of one of the sensors isdetermined in dependence on the time taken for respective signals fromone or more of the acoustic sources of known position to reach thesensor. In this respect, the positioning system operates very much likethe well known GPS system, except using acoustic signal such as sonarsignals. In this respect, to solve for an unknown position in threedimensions requires signals to be received from at least four knownacoustic sources, and the calculation involves finding the distance toeach of the sources.

However, in a preferred embodiment the calculating further comprisesforming a plurality of subsets of the acoustic sensors, a subset ofsensors comprising a virtual line array of acoustic sensors. A directionfrom a subset of sensors to an acoustic source of known position maythen be determined in dependence on a phase delay of receipt of anacoustic signal from the acoustic source across the acoustic sensors ofthe array. By finding direction to a source rather than distance to asource then the number of sources required for a position fix isreduced. Specifically, in one embodiment the position of a subset may bedetermined by detecting direction to n acoustic sources, where there aren degrees of freedom of movement of the sensors forming the subset.

In some embodiments the subsets of sensors may be contiguous along thefiber, whereas in other embodiments the subsets of sensors may overlap,such that any one acoustic sensor is a member of more than one subset.In this latter case, more positions of points along the fiber can beobtained, and hence spatial resolution is increased.

From another aspect an embodiment of the present invention provides amethod of vibration detection in a structure using an optical fiberdistributed acoustic sensor deployed in a known relationship withrespect to the structure such that a known part of the optical fibercorresponds to and moves with a known part of the structure. The methodin particular may comprise detecting backscattered light on the fiber,the backscattered light being dependent on strain induced in the fibredue to mechanical strain in the structure to which the fibre relatescaused by vibrations in the structure. Then, from the detectedbackscatter, a signal representative thereof is processed to determine afrequency of oscillation of the vibrations in the structure. Thebackscattered light may be Rayleigh and/or Brillouin light generatedalong an optical fibre.

With the above, an optical fiber based DAS can also be used to detectmechanical vibrations in a structure, for example vortex inducedvibrations.

In a preferred embodiment the same optical fiber distributed acousticsensor system is used to perform both vibration detection in accordancewith the above aspect, and position detection in accordance with thefirst aspect. No additional sensor system is therefore required in orderto perform both functions. In this respect, within a preferredembodiment frequency filtering of the signal detected by the opticalfibre DAS is undertaken to divide the signal into low frequencies andhigh frequencies, wherein the low frequencies (<100 Hz) are used forvibration detection, and the high frequencies (>1 kHz) are used forposition and/or shape monitoring.

In addition, in further embodiments the optical fiber DAS may alsoundertake passive acoustic monitoring. Such passive acoustic monitoringmay comprise detecting acoustic events having an energy greater than apredetermined energy threshold, and hence be used to try and detectcatastrophic failures, or cracking of the structure.

In preferred embodiments the structure is a subsea riser, or othersubsea structure such as a cable or mooring line.

The signal processing performed to obtain the acoustic output, anddetect position or vibration is usually performed in software by aprocessor which receives a data signal corresponding to or derived frombackscattered light from along the fibre. In a further aspect,therefore, there is provided a computer program or suite of computerprograms so arranged such that when executed by a computer they causethe computer to operate in accordance with the method of any of theabove aspects. Also provided is a computer readable storage mediumstoring a computer program or at least one of the suite of computerprograms.

From another aspect of the invention an embodiment provides a system formonitoring the position of a structure. The system includes an opticalfiber distributed acoustic sensor system deployed in a knownrelationship with respect to the structure such that a known part of theoptical fiber corresponds to a known part of the structure. The sensorsystem further comprises a processor arranged to use the optical fiberas a distributed acoustic sensor to detect, at a plurality of acousticsensor positions along the fibre, acoustic signals emitted by aplurality of acoustic sources deployed at known positions in an area inwhich the structure to be monitored is located The processor thencalculates relative positions of a plurality of the acoustic sensors independence on the detected acoustic signals from the acoustic sources;and from the calculated positions of the sensors along the fibre is thenable to further determine a shape, or shape and position, of thestructure in dependence on the known relationship between the fiber andthe structure.

Yet another aspect of the invention provides embodiments that detectvibration in a structure. Such systems comprise an optical fiberdistributed acoustic sensor system deployed in a known relationship withrespect to the structure such that a known part of the optical fibercorresponds to and moves with a known part of the structure. The sensorsystem further comprises an interferometer arrangement arranged todetect backscattered light on the fiber, the backscattered light beingdependent on strain induced in the fibre due to mechanical strain in thestructure to which the fibre relates caused by vibrations in thestructure. A processor in the sensor system is then further arranged,from the detected backscatter, to process a signal representativethereof to determine a frequency of oscillation of the vibrations in thestructure. The backscattered light may be Rayleigh or Brillouinbackscatter.

In a preferred embodiment, the same optical fiber distributed acousticsensing system is able to perform both position monitoring and vibrationdetection at the same time, using the same backscattered signal from thefibre.

In particular, in one embodiment the processor is further arranged tofrequency filter the signal detected by the optical fibre DAS into lowfrequencies and high frequencies, wherein the low frequencies (<100 Hz)are used for vibration detection, and the high frequencies (>1 kHz) areused for position monitoring.

In addition, in a further embodiment the processor is further arrangedto undertake passive acoustic monitoring. In such embodiments thepassive acoustic monitoring comprises detecting acoustic events havingan energy greater than a predetermined energy threshold.

In some embodiments the shape, or shape and position, of the structureis repeatedly determined so as to track changes in shape and/or movementof the structure with respect to time. This can provide severaladditional advantages, and in particular allows fatigue monitoring oranalysis of the structure in dependence on the tracked changes in shapeand/or movement of the structure to be performed.

Further features and advantages will be apparent from the appendedclaims.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages of the present invention will becomeapparent from the following description of an embodiment thereof,presented by way of example only, and by reference to the drawings,wherein like reference numerals refer to like parts, and wherein:

FIG. 1 is a diagram illustrating an operating environment of embodimentsof the invention;

FIG. 2 is a diagram of an interferometer apparatus used in embodimentsof the invention;

FIG. 3 is a diagram illustrating an operating environment of embodimentsof the invention;

FIG. 4 is a flow diagram of a first embodiment;

FIG. 5 is a flow diagram of a second embodiment;

FIG. 6 is a diagram illustrating how subsets of acoustic sensors canform virtual line arrays;

FIG. 7 is a diagram illustrating hoe phase delay along a line arrayvaries with angle of incidence of an acoustic wave;

FIGS. 8 and 9 are diagrams illustrating the operation of differentvariants of a third embodiment;

FIGS. 10 and 11 are respective flow diagrams illustrating the operationof the different variants of the third embodiment;

FIGS. 12 and 13 illustrate example resonant modes in a structuretethered at both ends;

FIG. 14 shows possible oscillation directions of a structure;

FIG. 15 is a diagram of an experimental rig forming a further embodimentof the invention;

FIGS. 16, 17, and 18 are graphs and other data showing the output of aDAS at different respective frequencies of oscillation of theexperimental rig;

FIG. 19 is a flow diagram illustrating the operation of a furtherembodiment of the invention;

FIG. 20 is a graph showing ambient noise spectra for the deep ocean. Lowfrequencies according to Knudsen, and molecular noise curve according toMellen. Reproduced from (Urick R. J., 1984).

FIG. 21 is a diagram showing the geometry of a line array after Urick(Urick R., 1983).

FIG. 22 is a series of graphs showing the effects of spatial resolutionand operating frequency on the directional gain of a DAS when employedin a straight-line configuration

FIG. 23 is a graph that shows that increasing the signal-to-noise ratioand number of snapshots allows high precision to be achieved in thepositioning algorithm.

DESCRIPTION OF THE EMBODIMENTS Overview of Embodiments

A brief overview of embodiments will first be given, followed bydescription of specific embodiments. Embodiments of the invention fallinto three classes, a first class relating to embodiments which performstructure position and shape determination using an acoustic positioningsystem, a second class relating to mechanical vibration detection in thestructure, possibly as resonant modes, and a third class which combinethe position and shape determination and the vibration detection intothe same embodiment. Within the described embodiments the structurebeing monitored is a subsea riser, and in preferred embodiments this isthe case. However, in other embodiments the structure may be any otherstructure or structure type, such as buildings, towers, chimneys,pylons, antennas, process plant, or any other structure.

FIG. 1 shows a typical riser deployment used in an embodiment of theinvention. Here, a riser 40 extends from a seafloor installation 42 suchas a well top, production facility or blow-out preventer to a surfacefacility such as a ship or rig 44. Substantially co-located with andextending along the length of the riser is an optical fiber cable 32.The cable 32 may be clamped to the outside of the riser, or in otherembodiments may be contained within the riser, or may alternatively bespiralled around the outer surface of the riser. Whichever configurationis adopted, there is a known relationship between any particular part ofthe optical fiber and a corresponding part of the riser, in that it isknown which part of the optical fiber is adjacent or connected to whichpart of the riser.

Also provided are a number of acoustic positioning system acousticsources 48, which are each at a known location and each emitrespectively identifiable acoustic signals, either continuously orrepeatedly.

The optical fiber cable acts as a distributed acoustic sensor.Distributed optical fiber sensors operate by launching a pulse of lightinto an optical fiber. This generates weak scattered light which iscaptured by the fiber and carried back towards the source. By timing thereturn of this backscattered light, it is possible to accuratelydetermine the source of the backscatter and thereby sense at all pointsalong a fiber many tens of kilometers in length. Three differentphysical mechanisms produce the backscatter, being Rayleigh, Brillouinand Raman scattering. A common instrument that uses the intensity of thebackscattered Rayleigh light to determine the optical loss along thefiber is known as an Optical Time Domain Reflectometer (OTDR). Rayleighbackscatter light is also used for coarse event/vibration sensing. Ramanlight is used by a Distributed Temperature Sensor (DTS) to measuretemperature, achieving a temperature resolution of <0.01° C. and rangesof 30 km+. However the response time of distributed temperature sensorsis typically a few seconds to several minutes. Distributed Brillouinbased sensors have been used to measure strain and temperature and canachieve faster measurement times of 0.1 second to a few seconds with aresolution of around 10 microstrain and 0.5° C.

In order to provide for acoustic sensing via the optical fiber in aparticular embodiment of the invention, described here in order toprovide an example of a preferred implementation of embodiments of thepresent invention, the optical fiber 32 is coupled to an interferometersuch as illustrated in FIG. 2 , located for example in the surfacevessel 44.

With reference to FIG. 2 , light emitted by a laser (21) is modulated bya pulse signal (22). An optical amplifier (25) is used to boost thepulsed laser light, and this is followed by a band-pass filter (26) tofilter out the ASE noise of the amplifier. The optical signal is thensent to an optical circulator (27). An additional optical filter (28)may be used at one port of the circulator (27). The light is sent tosensing fiber (32), which is for example a single mode fiber or amultimode fibre. A length of the fiber may be isolated and used as areference section (30), for example in a “quiet” location or with acontrolled reference signal. The reference section (30) may be formedbetween reflectors or a combination of beam splitters and reflectors(29) and (31). The reflected and the backscattered light generated alongthe sensing fiber (32) is directed through the circulator (27) and intothe interferometer (33).

Within the interferometer, the incoming light is amplified in an opticalamplifier (1), and transmitted to the optical filter (2). The filter (2)filters the out of band Amplified Spontaneous Emission noise (ASE) ofthe amplifier (1). The light then enters into an optical circulator (3)which is connected to a 3×3 optical coupler (4). A portion of the lightis directed to the photodetector (12) to monitor the light intensity ofthe input light. The other portions of light are directed along firstand second optical paths (5) and (6), with a path length differencebetween the two paths. Faraday-rotator mirrors (FRMs) (7) and (8)reflect the light back through the first and second paths (5) and (6),respectively. The Faraday rotator mirrors provide self-polarisationcompensation along optical paths (5) and (6) such that the two portionsof light efficiently interfere at each of the 3×3 coupler (4) ports. Theoptical coupler (4) introduces relative phase shifts of 0 degrees, +120degrees and −120 degrees to the interference signal, such that first,second and third interference signal components are produced, each at adifferent relative phase.

First and second interference signal components are directed by theoptical coupler (4) to photodetectors (13) and (14), and the thirdinterference signal component incident on the optical circulator (3) isdirected towards photodetector (15).

The photodetectors (12), (13), (14) and (15) convert the light intoelectrical signals. The electrical signals are digitised and then therelative optical phase modulation along the reference fiber (30) and thesensing fiber (32) is computed using a fast processor unit (34). Theprocessor unit is time synchronised with the pulse signal (22). The pathlength difference between path (5) and path (6) defines the spatialresolution.

Methods for calculating the relative phase and amplitude from threephase shifted components of an interference signal are known from theliterature. For example, Zhiqiang Zhao et al. (“Improved DemodulationScheme for Fiber Optic Interferometers Using an Asymmetric 3×3 Coupler”,J. Lightwave Technology, Vol. 13, No. 11, November 1997, pp. 2059-2068)and Huang et al (U.S. Pat. No. 5,946,429) describe techniques fordemodulating the outputs of 3×3 couplers in continuous wave multiplexingapplications.

The phase angle data is sensitive to acoustic perturbations experiencedby the sensing fiber 32. As an acoustic wave passes through the opticalfibre, it causes the glass structure to contract and expand. This variesthe optical path length between the backscattered light reflected fromtwo locations in the fiber (i.e. the light propagating down the twopaths in the interferometer), which is measured in the interferometer asa relative phase change. In this way, the optical phase angle data canbe processed to measure the acoustic signal at the point at which thelight is reflected.

An example system corresponding to the above and that is commerciallyavailable is the Silixa iDAS system, available from Silixa Ltd, Elstree,London, United Kingdom. The Silixa iDAS system uses the above describedinterferometer arrangement to accurately and rapidly measure theRayleigh backscattered signal with a precision and speed that allowsacoustic measurements. The iDAS is so sensitive that it allows digitalrecording of acoustic fields at every location along an optical fiberwith a frequency of up to 100 kHz.

In addition, by using digital signal processing, the acoustic responsealong the fiber can be combined to enhance the detection sensitivity bytwo-orders of magnitude, thereby exceeding the sensitivity of pointsensors as well achieving highly directional information. With the DAS,the fiber acts as an acoustic antenna whose sensitivity and frequencyresponse can be adjusted electronically by using different sensingconfigurations. For example, the fiber can be deployed in linear,directional or multi-dimensional array configurations. In addition, theprecision that the DAS can achieve uniquely allows the speed of sound inthe material surrounding the fiber to be accurately determined. Thisallows the DAS to detect, for example, the presence of gas in oil (anecessary step towards multiphase flow measurement).

In addition, further processing can be performed by processor 34 on thedetermined acoustic signal, for example to determine positioninformation or to detect mechanical vibrations in the structure to whichthe fiber is attached. Therefore, as also shown in FIG. 2 and pertinentto the present embodiments, also provided as part of the apparatus of anembodiment is a computer readable medium 36 such as a flash drive orhard disk, which stores an acoustic positioning program 362 and avibration detection program 364. As will be described later, theacoustic positioning program 362 is arranged to control the processor 34to process the determined acoustic data from the optical fiber DAS todetermine the position of the fiber, based on received acoustic signalsfrom known acoustic sources 48. In addition, the vibration detectionprogram 362 is arranged to control the processor 34 to process thedetermined acoustic data to look at significantly lower frequencies, andspecifically to detect low frequency resonant vibrations of the riserstructure, such as vortex induced vibrations. Such vibrations may notmake actual acoustic noise, but are detectable by the DAS using the samephysical mechanism of Rayleigh backscatter because as the fiber movesback and forth with the riser structure under the resonant vibrationthen parts of the fiber are placed under strain in the same manner as ifthey were within a vibro acoustic field. As such, the resonant vibrationmanifests itself in the DAS output in the same way as an acoustic inputto the sensor array, although at a significantly lower frequency.Further details of the vibration detection performed by embodiments ofthe invention will be given later.

Hence, as described above, using a DAS such as that described turns astandard single mode fiber optic cable into a transduction system whichfunctions like a string of hydrophones. The length and sensing densityof this virtual string of hydrophones is limited by a combination offactors, including the sampling frequency and spatial resolution. Forthe sake of the discussion here, a 10 km fiber can be monitored using aSilixa iDAS with a sampling frequency of 10 kHz and a spatial resolutionof about 1 m. Thus a single iDAS box can be used with a standard opticalfiber to give the equivalent output of 10,000 hydrophones.

Acoustic positioning technology has been in wide use throughout the oiland gas industry for several decades. Positioning systems function byobserving the signal from one or several controlled sources, andobserving either changes in relative phase or absolute time-of-flight todetermine the position of a receiver. This concept is unchangedregardless of the medium of interest and the radiation used to power thesystem. Thus an acoustic positioning can be conceptually similar to aGPS system in some implementations.

Given the capability of the DAS described above to turn a fiber into anarray of virtual hydrophones, it is possible to consider a fiber as astring of discretely spaced sensors. The output from each of thesesensors can then be manipulated just as one might for a standard sensor.In the case of a positioning system, this may involve observing thesignal from a controlled receiver to find the position of that receiver,based, for example, on the receiver receiving signals from acousticsources of known position. By doing this for each discrete acoustic zonealong the fiber, one can extract the position of each zone and henceinterpolate for the shape. If the position of each zone of the fiber isthen related to the position of each zone of another structure, such asa riser, in a known way (for example by being co-located and fixedthereto), then knowing the shape of the fiber also gives us informationof the shape of the structure, such as a riser, to which it is related.

In summary then, using an optical interferometer based DAS embodimentsof the invention are able to measure acoustic signals at approximately 1m resolution along the length of an optical fiber attached to a subseastructure, such as a riser. Combined with an acoustic positioning systemsuch as a long baseline system then the position of each segment of thefiber may be determined, and hence also the related position of thestructure. This therefore allows for shape monitoring of the structuresuch as riser to be undertaken, by interpolating between the foundpositions, and knowing the spatial relationship between the fiber andthe structure. Changes in the shape or shape and position of thestructure with respect to time may also be monitored, to deteimine howthe structure moves under various conditions, such as loadingconditions, or with movement of the surrounding environment (such asflows or vortices in the surrounding water, in the case of a riser). Inaddition, and advantageously, the fiber is also able to detect resonantvibrations of the structure, which occur at much lower, and generallyinaudible, frequencies, due to the expansion and compression of thestructure under the vibration being transferred to the fiber, and henceinducing strain in the fiber which affects the backscatter in a similarmanner to being placed in a vibro acoustic field.

In view of the above overview, several embodiments of the invention willnow be described.

Acoustic Positioning System for Shape Determination

FIG. 3 illustrates the operating environment of a first embodiment.Here, fiber 32 attached to or otherwise related in a known manner to asubsea riser (not shown) extends from surface vessel 44 to seafloorinstallation 42. The fiber 32 forms part of a DAS, as described above,that is able to sense an incident vibro acoustic field with a spatialresolution of approximately 1 m. Hence, an acoustic sensor 462 is formedapproximately every 1 m along fiber 32, to give n acoustic sensors alongthe length of fiber 32.

Also provided are x acoustic sources Xn (48), with four such sourcesbeing shown in FIG. 3 . Each acoustic source is at a known location, andemits an identifiable acoustic signal, for example at a specific, known,frequency, or of a particular pattern.

In a first embodiment of the invention, each sensor 462 is treatedindividually, and a respective location found for a particular sensorwithout reference to positions found for other sensors on the fibre.FIG. 4 illustrates the steps involved.

With reference to FIG. 4 , when running acoustic positioning program 362processor 34 acts to determine a position for each sensor 462 on thefibre, as noted, by initiating a FOR processing loop, at s.4.2. Withinthe loop for a particular sensor at s.4.4 the acoustic transmissionsfrom the acoustic sources Xn (48) are respectively detected, andrespective time of flight for each transmission found, to give a set oftime data tn. The time of flight for each acoustic signal can then beconverted, by knowing the local speed of sound in water, into a distancefrom each sensor 462 to each source Xn. By then knowing the respectivedistances to each source Xn, and the known positions of each source Xn,at s.4.6 it then becomes possible to calculate the relative position ofa particular sensor 462 relative to the positions of the sources Xn. Ats. 4.8 this position data is stored for sensor n, and at step 4.10processing proceeds to the next sensor 462 on the fibre. Once a positionhas been found for all of the sensors 462 on the fiber 32, theprocessing loop ends.

At this point in time, therefore, the processor memory contains positiondata for each sensor point 462 along the entire length of the fibre,relative to the known positions of the acoustic sources 48. By knowingthat the sensors are connected together by the fibre, the shape of thefibre can be found by interpolation between the found three dimensionalspatial positions of the sensors. Moreover, because there is a knownspatial relationship between the fiber and any riser to which it isconnected or otherwise related, the shape and position of the riser canalso be determined. As such, provided the position sampling rate issufficiently high then movement and changes of shape of the fibre, andhence the riser, can be tracked over time. Tracking movement and changesin shape of the riser allows for monitoring and other analysis, such asaccurate fatigue analysis, amongst other things, to be performed inrespect of the riser.

A second embodiment that improves upon the first embodiment will alsonow be described. The second embodiment takes the same operatingenvironment of FIG. 3 as described previously, and operates in a similarmanner to the first embodiment, except that within the second embodimenta priori knowledge that the sensor are actually distributed in an arrayalong the fiber is employed as a sense check on a determined position.That is, given that the sensors are 1 m apart along the fibre, theposition found for the nth sensor should be no more than 1 m away fromthe position found for the (n−1)th sensor. Hence, a check can beperformed that a determined position is no more than 1 m away from apreviously determined position, as the sensors are processed one by onealong the fibre. FIG. 5 shows the procedure.

With reference to FIG. 5 , when running acoustic positioning program 362processor 34 acts to determine a position for each sensor 462 on thefibre, as noted, by initiating a FOR processing loop, at s.5.2. Withinthe loop for a particular sensor at s.5.4 the acoustic transmissionsfrom the acoustic sources Xn (48) are respectively detected, andrespective time of flight for each transmission found, to give a set oftime data tn. The time of flight for each acoustic signal can then beconverted, by knowing the local speed of sound in water, into a distancefrom each sensor 462 to each source Xn. By then knowing the respectivedistances to each source Xn, and the known positions of each source Xn,at s.5.6 it then becomes possible to calculate the relative position ofa particular sensor 462 relative to the positions of the sources Xn. Ats.5.8 a check is then performed, provided the present sensor is not thefirst sensor on the fibre, as to whether the determined position iswithin an allowable distance of the previously determined position forthe previous sensor in the fiber array. For example, that the presentlydetermined position is no more than 1 m from the previously determinedposition. If this check is met, then at s. 5.10 the position data isstored. If it is not met, then processing returns to step 5.4, andanother position is calculated for present sensor n. The processing loopproceeds in this manner until a position has been found for all thesensor points 462, and then the processing ends.

As with the first embodiment, at this point in time, therefore, theprocessor memory contains position data for each sensor point 462 alongthe entire length of the fibre, relative to the known positions of theacoustic sources 48, and hence the shape of the fibre, and of anystructure to which it is attached, can be determined.

Thus far, the second embodiment has made use of the fact that thesensors are connected in a line array in a limited way only, to performa sense check on a determined position. In the first embodiment, no usewas made of this a priori information. In the preferred thirdembodiment, however, much greater use is made of the fact that thesensors are connected in a line array, in order to be able to finddirection to a particular acoustic source 48, rather than simplydistance. By finding direction to a source, fewer sources are requiredto find a position, specifically as many sources as there are degrees offreedom of movement of the sensor.

FIGS. 6 and 7 illustrate the concept of the third embodiment.Specifically, contiguous groups of sensors 462 along the fiber 32 aregrouped together into a virtual small line array sensor 62. An incidentacoustic wave incident on the line array sensor 62 will cause an outputfrom each of the sensors at different times, dependent on the angle ofincidence of the wave. Hence, as shown in FIG. 6 , an incident wave 64incident on line array 62 at the angle shown will first cause a signalfrom sensor 622, followed by sensor 624, 628, and finally 630. Moreover,the time delay 6 between each sensor being triggered is a cosinefunction of the direction of travel of the wave, whereby the angle ofincidence of the wave can be determined from the order in which thesensors give an output and the time delay between sensor outputs alongthe array. In this respect, it is assumed that the array size is smallenough so as to be considered to be in the far field of the incidentwave.

FIGS. 8 and 9 illustrate the application of the above in the thirdembodiment. In FIG. 8 , a plurality of contiguous virtual small linearray sensors m_(n) 62 are formed along the fiber 32. When a signal froman acoustic source 48 is incident thereon, each array is able todetermine a direction to the source using the phase delay of theincident wave across the small array, as described above. In Figure thearrays are contiguous, such that if there are, say, 5 sensors in eacharray, then there are n/5 virtual small line arrays formed. However,because a single direction is found for each array, it might be the casethat this does not give a high enough spatial resolution for the shapemonitoring (it would give a position for every 5 m array, rather thanevery 1 m). Therefore, if more position points are found, additionalvirtual small line arrays may be found by overlapping the arrays, asshown in FIG. 9 . Thus for example, each sensor point 462 may be amember of more than one, and up to several, virtual small line arrays62. A direction to a source can be found for each small line array.

Moreover, the small line arrays are virtual because they are formedsimply by processing the signals from the sensors 462 that are membersof an array together. Hence, the virtual arrays may overlapsignificantly by having many of the same sensors as members.

FIGS. 10 and 11 illustrate two ways in which the virtual small linearrays may be used to find position data for the whole fibre. In theembodiment of FIG. 10 , when running acoustic positioning program 362processor 34 acts to determine a position for each line array m on thefibre, as noted, by initiating a FOR processing loop, at s.10.2. Withinthe loop for a particular line array at s.4.4 the acoustic transmissionsfrom the acoustic sources Xn (48) are respectively detected, andrespective directions to the sensors found. The position of each linearray can then be found, by taking the position solution which fits toall the found direction solutions. At s. 4.8 this position data isstored for line array m (62), and at step 4.10 processing proceeds tothe next array m on the fibre. Once a position has been found for all ofthe line arrays on the fiber 32, the processing loop ends. Note that theline arrays may be contiguous, as shown in FIG. 8 , or overlap, as shownin FIG. 9 .

At this point in time, therefore, the processor memory contains positiondata for each line array 62 along the entire length of the fibre,relative to the known positions of the acoustic sources 48. By knowingthat the line arrays form part of the fibre, the shape of the fibre, andhence any riser to which it is connected or otherwise related, can bedetermined, by examination of the found three dimensional spatialpositions of the line arrays. As such, provided the position samplingrate is sufficiently high then movement and shape of the fibre, andhence the riser, can be tracked over time.

FIG. 11 illustrates a further embodiment being a modification of theembodiment of FIG. 10 . Here, s.11.2 to 11.6 are the same as steps. 10.2to 10.6 described above, but at s. 11.8 a position sense check isperformed to determine whether the calculated position for an array isallowable given the already determined position of the previous array.For example, it will; be known in advance what will be the maximumdistance between the same points, e.g. the centre of each array. Forcontiguous arrays this may be, for example, 5 m, whereas for overlappingarrays it may be less, say 1 m or 2 m. Hence, if it is determined thatthe determined position of array m is too far from the positionsdetermined for array (m−1), then the position for array m is calculatedagain. In this way, a sense check is performed as the array positionsare found along the fibre.

Once a position has been found for each array then at that point in timeit becomes possible to determine the shape of the fibre, and hence anystructure to which it is attached. Moreover, by taking position samplesat a high enough rate then movement of the fiber (and hence thestructure) can be monitored.

Further operational considerations for the acoustic positioning systemof the above described embodiments will now be described.

The operating limitations for sonar systems can be understood using theSonar EquationSL−TL>NL−DI+DT  1.where SL is the Sound Level of the source, TL is the transmission lossthrough the medium, NL is the noise level, DI is the Directivity Index,and DT is the Detection Threshold. All units here are in decibelsrelative to the standard reference intensity of a 1 μPa plane wave. Eachof these quantities is now considered individually. This analysis usesthe method well-known to practitioners of underwater acoustics asdescribed in by Urick (Urick R. J., 1967).Sound Level

The projector to be used for this system should be an off-the-shelftransducer. Anticipating that the system will work best at lowfrequencies and high power (as per the analysis to follow), Silixasuggests 180 dB re 1 μPa as a working number for the sake of this study.This level would be high, but not unreasonable, for a low frequency,long baseline (LBL) system of the type used in deep water positioning.

Transmission Loss

Transmission loss in the water comes from two principal sources:propagation spreading and material loss. Spreading is the term used todescribe the effect of the reduction in signal level which occurs fornon-planar sound as the signal diverges along its propagation path.Since the same sound energy must cover successively larger ‘shells’ overtime, the signal intensity over a given area reduces with distance fromthe source. This can be characterized as described in the table below.

TABLE 1 Transmission loss as a result of geometric spreading Intensityvaries Transmission Spreading type with radius r as loss (dB) None r⁰ 0Cylindrical r⁻¹ 10 log r Spherical r⁻² 20 log r

For propagation in the ocean, it is appropriate to assume sphericalspreading. Therefore, the transmission loss caused by spreading has beenassumed to be 20 log r for the sonar equation calculations shown laterin this document.

Along the propagation, transmission loss as a result of material lossespath increases with frequency. This can be approximated using the methodof (Thorp, 1966).

$\begin{matrix}{\alpha = {\frac{0.1f^{2}}{1 + f^{2}} + \frac{40f^{2}}{4100 + f^{2}} + {2.75 \times 10^{- 4}f^{2}} + {0.003.}}} & 2\end{matrix}$where f is frequency and α is absorption in units of dB per kiloyard.This equation indicates why most LBL systems work at low- andmid-frequency. The increased absorption at higher frequencies results inlower SNR when operating in that regime.Noise Level

There are two principal sources of noise in the proposed system:self-noise from the DAS system, and oceanic ambient noise. In the belowthe noise from the DAS is assumed to be roughly as loud as the noisyambient sea.

The subject of ambient noise level in the sea has been a topic ofinterest to researchers in both shallow and deep water for severaldecades. The classic starting point for modern discussions on ambientnoise in deep water are the well-known Knudsen curves (Knudsen, Alford,& Emling, 1948), which show how the ambient noise spectrum varies withsea state. The work of Knudsen indicates a descent in noise at a rate ofabout 20 dB/decade above about 100 Hz. While this trend is well suitedfor low frequency noise estimation (though it should be noted thatKnudsen neglected the effect of rain-induced bubble entrainment in therange of 14 kHz), but for frequencies above about 50 kHz, thermal noiseis usually considered to be a significant source of disturbance (Mellen,1952). The degree to which the thermal noise work of Mellen is relevantto the present invention is still unclear, but it is nonethelessincluded in the spectrum shown in FIG. 20 to counter the apparentconclusion from Knudsen that noise always decreases with increasingfrequency.

For the calculations performed here, Beaufort State 5 (winds 18-24 mphwith many whitecaps visible) has been assumed.

Directivity Index

Directivity index is usually treated as an advantage in the sonarequation, as it can be used to reduce the volume over which the acousticsignal spreads. However, if the receiver in a system of the type usedfor this application (known as a passive monostatic system) is orientedsuch that the transducer is oriented away from the direction ofpropagation, then the directivity can be a disadvantage. For retrofitinstallations where the cable is orientated along the riser and at longranges from the transponders, where the cable is essentially parallel tothe path of propagation, that is indeed the case. The receiver, theoptic fiber DAS, is in effect what is known as a continuous line array.The directivity for a continuous line array is well-known, and shown inFIG. 21 .

Urick calculates the voltage output V for a line array of length L(illustrated above) by considering the contribution of a differentialelement as

$\begin{matrix}{{dV} = {\frac{R}{L}e^{{(\frac{j\; 2\pi}{\theta})}{x \cdot \sin}\;\theta}d\;{x.}}} & 3\end{matrix}$where the quantities are as illustrated in 21. The total voltage canthen be calculated by integrating over the length of the array.

$\begin{matrix}{{d\; V} = {\frac{R}{L}{\int_{- \frac{L}{2}}^{\frac{L}{2}}{e^{{(\frac{j\mspace{11mu} 2\pi}{\theta})}{x \cdot \sin}\;\theta}d\;{x.}}}}} & 4\end{matrix}$

The beam pattern b(θ) will be the square of V normalised so that themaximum of b(θ)=1, which gives the well-known result

$\begin{matrix}{{b(\theta)} = {\left( \frac{V}{R} \right)^{2} = {\left\lbrack \frac{\sin\left\lbrack {\left( \frac{\pi\; L}{\theta} \right)\sin\;\theta} \right\rbrack}{\left( \frac{\pi\; L}{\theta} \right)\sin\;\theta} \right\rbrack^{2}.}}} & 5\end{matrix}$

Since the system will be receiving signal along the length of the riser,and hence away from the main lobe, it is informative to apply theminimal averaging length in order to overcome the signal suppressionwhich will result. Currently, the minimum Silixa iDAS resolution is 50cm. Further, the undesired suppression can be minimized by increasingthe wavelength of interest. To illustrate the combined result of thesetwo factors, the directivities for 1 m and 50 cm systems operating at 10kHz and 50 kHz have been shown in FIG. 22 .

FIG. 22 can be studied in the context of this discussion by consideringthe worst-case scenario shown in each figure, as the highest suppressionfor a receiver of this type occurs at endfire (that is, where the signalray is oriented along the length of the receiver). For the 1 mresolution, the 10 kHz and 50 kHz cases respectively give −46 dB and −55dB suppression at endfire(90°), while for the 50 cm resolution, 10 kHzand 50 kHz result in −32 dB and −54 dB respectively. These findingsillustrate the outcome expected when considering the derivation above:for the application at hand, it is optimal to use as fine a DAS spatialresolution as can be delivered, and a driving signal with as low of acenter frequency as is possible. Note that a reduction in drivingfrequency will result in a corresponding increase in background noiselevel as per the previous discussion on ambient noise, but that theresultant benefits in directivity drive the optimal driving frequency tothe region of about 1 kHz. For the purpose of the calculation performedbelow, a 50 cm resolution and 10 kHz operating frequency are assumed,giving a directional suppression of −32 dB.

It should be noted that creative fiber installations, such as thosetaking advantage of spiral cable geometries, could be used to overcomesome of the challenges introduced as a result of geometric signalaveraging.

Detection Threshold

Dynamic positioning of a cable via an optic fiber DAS as described inthe above embodiments can be performed using the same signal processingtechniques that are used with standard hydrophones as discussed above.This section is used to perform an analysis which helps to identify thepractical factors which are most critical in determining a practicalSignal-to-Noise (SNR) ratio via an analysis of the system. This SNR canthen be set as a Detection Threshold in the sonar equation. Since thesystem is taking advantage of the power offered by having a large set ofsensors, and not just a single sensor, it is advantageous to use anarray processing method. Further, the problem is well constrained, asthe upper and lower termination limit of the riser are possibly at aknown location. An additional refinement can be made because the roughshape of the riser can be estimated. The analysis here begins with thesolution of Fistas and Manikas (Fistas & Manikas, 1994) (applicable tothe case where no assumptions are made concerning the riser shape), andthen incorporates geometric assumptions by employing the method of Kamil(Kamil, 2011). Finally, the method of Kamil is used to estimate themaximum horizontal system resolution. In this discussion, two types ofresolution are relevant: vertical resolution, and horizontal resolution.Vertical system resolution refers to the effective sensor spacingenforced by the DAS. Horizontal system resolution is the positioningprecision that results from the calibration algorithm. It should benoted that the analysis here is based on the use of three simultaneouslypresent sources, at least two of which operate at different azimuthangles.

If a source is transmitting from a known location to an array, thesignal received by an array of N sensors can be modeled as:x =√{square root over (P_(s))} S +n  6.where S is the manifold vector or source positioning vector (SPV). TheSPV is a mapping of the source locations to different phase delays andgains in the signals received by the array. P_(s) is the power of thetransmitted signal at the array's reference point and n is the noisevector.Far Field

Consider a source transmitting a narrowband signal from a known locationwhere the range ρ₀ from the array reference point satisfies thefollowing relation:

$\begin{matrix}{\rho_{0} ⪢ {\frac{2D^{2}}{\lambda}.}} & 7\end{matrix}$where D is the largest dimension of the array or the array aperture andλ is the wavelength. This source is considered to be in the far-field ofthe array. Thus, the amplitude of the received signal is approximatelyconstant across the array (this is particularly a valid assumption if weconsider short section of the riser (as can be seen from the far fieldcondition)). In the far-field case, the SPV used in Equation (6) can bemodeled as:S =exp(−j r ^(T) k )  8.where {tilde over (r)} is an 3×N matrix containing the locations of thesensors (in 3D) in the array. From Equation (7), it can be seen that themagnitude of the manifold vector is √{square root over (N)}.

If the sensor locations are imperfectly known, S can be used to denotethe nominal SPV (with assumed locations). Using Equation (7), the trueSPV Ŝ which takes into account the errors in the nominal values can bemodeled as:{circumflex over (S)}=exp(−j {tilde over (r)} ^(T) k )Θ Sdiag(exp(−j{circumflex over (r)} ^(T) k )) S    9.{tilde over (r)} is a matrix that contains the uncertainties in thearray sensor locations, whereas diag(V) denotes a diagonal matrix with Vin its diagonal elements. The superscript (□)^(T) denotes transpose ofthe vector or the matrix.

From Equations (6) and (7), it can be seen that the amplitude of thesignal does not have any information regarding the locations of thesensors. Therefore, the phase delay information is used to calibrate thearray and the power of the signal P_(s) can be assumed without loss ofgenerality to be equal to unity. The covariance matrix of the receivedsignal can be modeled as:R _(xx) =ŜŜ ^(H)+σ² I   10.where σ² is the noise power and I is the identity matrix. Also, thesuperscript (□)^(H) denotes conjugate transpose of the vector or thematrix.

The knowledge of the source location translates into knowledge of thenominal SPV (based on the assumed sensors locations) i.e. the nominalphase delay information. This is useful in estimating the actual sensorlocations. In particular, the covariance matrix is pre- andpost-processed by the diagonal matrix Λ defined asΛ=diag( s )  11.and is obtained from knowledge of the source location. Using Equation(10), this operation can be simplified to

-   -   12.

It is common to regard one element as a reference and to assume that itsposition is accurately known. For simplicity, the first element of thearray is taken as the reference element (Note that if this assumption isnot satisfied, the estimated array locations will have a translationalerror dependent on the position of the 1^(st) sensor node). Therefore,the vector exp(−j{tilde over (r)} ^(T) k) can be modeled as

$\begin{matrix}{{\exp\left( {{- j}\;{\overset{\sim}{\underset{\underset{\_}{\_}}{r}}}^{r}\underset{\_}{k}} \right)} = {\begin{bmatrix}1 \\\underset{\_}{u}\end{bmatrix}.}} & 13\end{matrix}$where u=exp(−j{tilde over (r)} ^(T) k)|₂₋₁ corresponds to the N−1elements of the vector exp(−j{tilde over (r)} ^(T) k) starting from thesecond element. Thus, equation (12) can be written as

$\begin{matrix}{{{\underset{\underset{\_}{\_}}{A}}^{H}{\underset{\underset{\_}{\_}}{R}}_{xx}\underset{\underset{\_}{\_}}{A}} = {\begin{bmatrix}{1 + \sigma^{2}} & {\underset{\_}{u}}^{H} \\\underset{\_}{u} & {{\underset{\_}{uu}}^{H} + \sigma^{2}}\end{bmatrix}.}} & 14\end{matrix}$

It can be seen from the above that one source can be used to estimatethe perturbations in the SPV (i.e. exp(−j(_(_r)^(−T)T_k)). However, weare more interested in the perturbations in the actual locations i.e.{tilde over (r)}.

From the knowledge of exp(−j{tilde over (r)} ^(T) k) the perturbationscan be estimated directly as the following:exp(−j{tilde over (r)} ^(T) k )=exp([{tilde over (x)} {tilde over (y)} z] k )= b   15.

The previous equation comprises a set of N−1 equations to solve d(N−1)unknowns where d is the dimension of the coordinate system in which weare interested (3 in the previous equations). The problem is strictlywell posed and comprises a system of over-determined equations ifM≥d  16.

For example, if for a given array geometry uncertainties can only occurin one dimension, one source is sufficient to estimate theuncertainties. However, for systems with two degrees of freedom (forinstance lateral motion and depth), a minimum of two sources are neededto be able to perform positioning accurately. Further increasing thenumber of sources beyond the problem dimensions d will improve theaccuracy of the estimates.

Near Field

The previous analysis can be used to estimate the sensor positionsassuming that the far field model is valid. To enforce this conditionfor the purpose of riser monitoring, the array of sensors has to bedivided into smaller sub-lengths along which the far field model can beapplied. In (Kamil, 2011), this analysis is extended to near fieldsources. The principle of operation is similar however, by using thenear field model; the amplitude information of the source can be used inaddition to the phase information to estimate the source location.Combining these two methods can in general result in much more accurateresults and faster convergence rates.

The result of a simulation showing the effect of signal-to-noise ratio,and the number of snapshots used to calculate position is shown in FIG.23 . In this figure, only two sources are used to calibrate an array of7 sensors. The presented root mean square error is the sum of the RMSEerrors in all the 7 sensors. Note that this calibration method has notused any noise reduction technique (e.g. spectral subtraction, Wienerfiltering etc.) which can be expected to result in an additional SNRgain of 10-20 dB. The numbers in the legend of the Figure indicate thenumber of snapshots (samples) used in the calibration calculation. A 10kHz transponder using signals of length 20 cycles (20 ms) sampled at 20kHz gives 400 samples per ping, meaning that at least 400 snapshots areachievable per transponder ping

It has been shown that high levels of precision in acoustic positioningcan be achieved, particularly when taking advantage of the fact that aDAS senses not just a single point in space, but an entire array ofsubsequently adjacent receivers. The simulation here has been performedin the case where the system is being run from startup. In the casewhere data is being continuously updated, the same analysis shows thatsimilar levels of precision can be achieved for fewer pings, but this isagain a function of the signal to noise ratio.

The output from both simulations indicates that a key factor in thedetermination of the system precision has to do with signal-to-noiseratio. The way in which this factor can be controlled is a topic ofdiscussion next.

As stated above, precision on the order of centimeters is achievable inthe acoustic positioning paradigm. It was also seen that the realizableprecision is a function of the signal to noise ratio. The signal tonoise ratio is actually controlled by the frequency sensitivity, whichis in turn a function of both structural considerations as well asdirectivity for reasons given below.

Even given an acoustically sensitive cable, an unsympathetic cablehousing or mounting method will render an optical fiber DAS unable toobserve acoustic signals with a SNR sufficient for accurate positioning.This is particularly important when considering the fact that it may bedesirable to implement the shape monitoring method of embodiments of theinvention on already-existing cables housed within heavily armoredumbilical lines. In this configuration, the degree to which the systemwill be able to observe the signal of interest is currently unknown. Itshould be born in mind that the structural sensitivity is a function offrequency, and so simply because a given umbilical is insensitive to aparticular positioning transducer, it cannot be assumed that it isinsensitive to all transducers. Nonetheless, for present purposes it isadvisable to use a cable of both excellent acoustic sensitivity and highwear in challenging environments. Further, such a cable should beinstalled in a way so as to avoid the undesirable effects of directionalsignal suppression.

Sonar Equation Model

By considering each of the parameters discussed in the context of thesonar equation, and generating a model on their basis, it can beestablished whether it is possible to use the optic fiber DAS acousticpositioning capability in the field, and to what range. The result ofthis exercise is shown below in Table 2. (assuming 50 cm spatialresolution, and a modest source directivity of 3 dB). In the first row,the SNR has been reduced to 10 dB (assuming knowledge of the transducerping signal, this could be achieved via a Wiener filter). In the secondrow, the SNR has been reduced to the level required in the case wherethe system is effectively ‘blind’ e.g. No knowledge concerning thetransducer signal is available. In the right hand column is calculatedthe maximum range for the case where an operating frequency of 50 kHz isused with an SNR of 10 dB.

Maximum f TL TL TL TL NL range (kHz) SL Spreading Absorption CableCombined Combined DI DT (m) 10 180 79 9 6 94 46 −29 10 9000 10 180 66 26 74 46 −29 30 2000 50 180 64 22 6 91 46 −29 10 100

It is clear from the above that the greatest deficit to systemperformance in this scenario is the directivity index resulting from thefiber configuration. Custom cables can be provided which can overcomethis challenge.

Distributed Temperature Sensing

Important to the acoustic propagation model used in the positioningembodiments described above is an estimate of the sound speed profilewithin the water column. This can also be sensed via an optical fiberbased system, such as that commercially available from Silixa Limited,Elstree, United Kingdom, and known as the Ultima distributed temperaturesensor (DTS). The DTS system supplied by Silixa can function in parallelwith the optic fiber DAS along a multimode fiber within the same cable,and gives the temperature with a resolution of 0.01° C. every 25 cm. Thetemperature sensor is an important component of the subsea distributedacoustic positioning system of the above embodiments, to give a watercolumn temperature profile from which the speed of sound in the watercan be deduced. It should be noted that, in a purpose designed cable, itis straightforward to introduce both multimode mode and singlemodecable. This will enable spatially coincident temperature and acousticsmeasurements respectively via a single efficient package.

Dynamic Vibration Modelling

A further embodiment of the invention will now be described in moredetail, relating to using the optic fiber DAS for detecting vibrationsin the structure to which the fiber is attached. This embodiment wasmentioned previously in the overview section above.

As discussed previously, an optic fiber DAS, such as the Silixa iDAS, isa vibroacoustic sensor which can report the dynamic field at intervalsof one meter along the entire length of a fiber optic cable up toseveral kilometers in length. In the previous embodiments it was shownhow such a sensor could be used as the sensing mechanism for adistributed acoustic positioning system based on acoustic signal outputat tens of kilohertz. In the present embodiment we describe how the samefiber being used for acoustic positioning sensing can simultaneously beused for dynamic vibration monitoring.

Consider a fiber optic cable suspended between two clamps and impartedwith a mechanical impulse. The mechanical impulse will introduce astrain which can be observed using a differential strain measurementmethod. The dynamic range of a DAS, such as the Silixa iDAS, allows itto measure differential strain, and it can therefore observe the timehistory of this strain disturbance. If for instance this dynamic strainhas a center frequency on the order of Hz, and this same cable isimparted with sound of a higher frequency (say, on the order of kHz),then a simple series of band pass filters can be used to distinguish thevibration-induced strain from the acoustic excitation. In this way, itis possible to facilitate both vibration monitoring and acousticpositioning along a single fiber. Hence the optic fiber DAS can be usedto detect low frequency resonant type vibrations in structures such asrisers, buildings, antenna towers, or any other large structure whichmay have resonant vibration modes. Other, non resonant, mechanicalvibrations may also be detected.

FIGS. 12 and 13 give examples of possible resonant modes of a structuresuch as a riser. FIG. 12 shows a higher order mode, and FIG. 13 shows afundamental resonant mode. In the case of a riser the structure istethered at the top and bottom, and hence resonates substantially like aguitar string (although of much lower frequency). Structures tethered atone end, such as a tall building or tower may simply resonate by swayingfrom side to side. In addition, any structure may also be subject tonon-resonant mechanical vibrations, which may also be detected by thepresent embodiments.

In the previous embodiments relating to acoustic positioning, it wasmentioned that the installation of fiber optic cable, and particularlythe cross-section of the assembly suspending that cable, will influencethe sensitivity of that fiber to the acoustic field. The same principalholds true for vibration monitoring, but the present embodiment relatingto vibration sensing is more robust to the specifics of cable designthan is the case for acoustic sensing. For instance, as an exampleembodiment, consider an armored optical cable suspended within a subseaumbilical line, where the umbilical has multiple additional layers ofarmor. The umbilical cable in this example embodiment is suspended byclamps mounted on the exterior of the riser cross-section, such that thewalls of the umbilical are in direct contact with the ocean. The clampsare at intervals of approximately 10 m. High frequency signals passingfrom the environment to the fiber are likely to be highly attenuated inthis scenario. However, the umbilical is actually very well-coupled tothe riser from a vibration standpoint. In this context, ‘well-coupled’means that the fundamental mechanical resonance of the clamp is manyorders of magnitude higher in frequency than the vibrations of interest.As a result, the clamp will tend to behave in the mass-controlled motionregime, which is essentially quasi-static. Further, the low ratio of thecable cross-sectional mass to that of the riser dictates that forwavelengths much longer than the inter-clamp spacing, high sensitivitysensing can be achieved on the cable. In this respect, the physicalsampling of systems is similar to the digital sampling of temporalevents, in that at least two points per cycle are needed to resolve awave. For a clamp spacing of 10 m, it is suggested that an optic fiberDAS such as the Silixa iDAS could be able to resolve waves as short as30 m.

An example test embodiment to test the functionality of such a vibrationsensor is shown in FIG. 15 . A key motivation for this experiment wasestablishing the degree to which vibrations below about 1 Hz can besensed using an unmodified DAS. The rig designed was made to resemble ariser with optical fiber cable mounted along its length. The cable waslaid along a hose length 150 in four runs 152 and joined to the flexiblehose using cable ties at 1 m intervals. The four separate runs ofoptical cable 152 were distributed radially as indicated in FIG. 15 ,with one run each at 0°, 90°, 180° and 270°. The purpose of usingmultiple cable runs was to demonstrate that the optic fiber DAS iscapable of determining the sections in compression and tensionsimultaneously. The hose was suspended from a height of 4 m using nylonrope 154. The optical cable used for these experiments was hermeticallysealed cable of the type appropriate for a deep-sea installation. Theenergy input for this test was provided by means of an engineer whodisplaced the cable in the horizontal plane with a zero-to-peakamplitude of approximately 1 diameter at the following frequencies: 0.5Hz, 0.05 Hz, and 0.0083 Hz (the last frequency corresponding to a periodof 2 minutes).

It should be noted that, for the purpose of this feasibility study, nomodifications were made to the optic fiber DAS to increase itssuitability for low frequency measurements.

The results of this experiment are shown in FIGS. 16, 17 and 18 , whichrespectively show the results for a driving vibration at 0.5 Hz, 0.05Hz, and 0.0083 Hz. Several interesting features of the system arerevealed by the experiment. At 0.5 Hz (see FIG. 16 ), the output isclearly evident in both the time and frequency domains. Thesignal-to-noise ratio of the results in the time domain appears todecrease with frequency. This is a result of two factors: driving methodand optical algorithm performance. The driving method used for theseexperiments was purely manual. That is, to drive the hose, an individualwith a stop-watch slowly manipulated the experiment at the mid-sectionbetween the clamps. This method is significantly easier to control at0.5 Hz than at 0.05 Hz and below, as no apparent rhythm is availablebelow about 0.5 Hz. As a result, the input signal at the lowestfrequencies is not truly sinusoidal, and some signal distortion exists.Despite the decrease in signal-to-noise ratio with frequency in the timedomain, the frequency domain results indicate clear detectability of the0.05 Hz (see FIG. 17 ) and 0.0083 Hz (see FIG. 18 ) signals. Thepresence of some harmonics is expected as per the input signaldistortions described above. A decrease in signal amplitude is seen withfrequency. In addition, at frequencies below about 0.1 Hz, temperaturedrift occurs over the cable as a function of time. It is likely in thefuture that signal processing improvements can be made to improve thedetection of such low frequencies by an optic fiber DAS.

From the above, however, it becomes apparent that an optic fiber DASsuch as the Silixa iDAS that is deployed to perform acoustic sensing canalso be used, with no modification, to detect low frequency mechanicalvibrations in a structure to which the fiber is attached. This isbecause the physical effect on the fiber in terms of altering Rayleighbackscatter is obtained whether the fiber is within a vibro acoustic(sound) field, or whether it is subject to actual mechanical vibration(which may or may not be accompanied by acoustic vibration). Thus, insome embodiments of the invention, and as shown in FIG. 19 , the DASsignal from the fiber (s.19.2) may be frequency filtered (s.19.4), forexample by respective band pass filters or low and high pass filters tosplit the signal into low frequencies (s.19.8) and high frequencies(s.19.14), the low frequencies typically being of the order of a few Hzand resulting from mechanical vibrations in the structure, and the highfrequencies being typically in the kHz range, and resulting from thefrequencies used by the acoustic sources 48 in an acoustic positioningsystem. The low frequencies are then used at s. 19.10 and 19.12 toperform vibration detection in the structure to which the fiber relates,and vibration data such as mode, and frequency can be obtained. The highfrequencies are used at s. 19.16 and 19.18 to perform acousticpositioning in accordance with any of the previously describedembodiments, to obtain data relating to the position of the structure towhich the fiber relates, and its shape. Moreover the two systems cancomplement each other, in that, whilst the vibration detection systemmay detect the presence of vibrations and their frequency, it will notnecessarily detect the direction of oscillation of the vibration. Inthis respect, as shown in FIG. 14 a structure tethered at both ends mayoscillate in any direction. However, by combining the output data of thevibration detection with the location and shape data from the acousticpositioning system, then knowledge is also obtained as to vibrationoscillation direction. Such information should prove useful in fatigueanalysis of the structure.

In addition, in some embodiments of the invention, in addition toacoustic positioning and vibration detection, the optical fiber DAS canalso provide passive acoustic data relevant to the structural health ofthe structure to which the fiber relates, as shown at s. 19.6. Thiscapability can be used to identify for instance high amplitude eventslinked to crack propagation or, where the structure is a riser, risersupport disengagement. The technology can be enabled via a thresholdingmethod, wherein events of energy in a particular frequency bandexceeding a given threshold trigger alarms which can be stored andlistened to by an operator, and linked with any changes in the physicalshape of the structure given by the position sensing embodimentsdescribed above.

Whilst the embodiments described above may be used with almost anystructure, particular embodiments are directed at the case where thestructure is a subsea riser, and hence below we consider severalinstallation issues of installing the optic fiber DAS on risers ofdifferent types.

Installation Issues

The way in which the a DAS-based riser monitoring system is installedand applied will vary between riser types. Next, a brief discussion ofeach of the main types of risers is given along with a description ofthe way in which an optic fiber DAS can be used for that riser. It hasbeen clearly stated where particular challenges arise as a result of theriser configuration. Note that these issues apply to the installation ofthe fiber generally, and hence to both the positioning and vibrationdetection embodiments.

Steel Catenary Riser (SCR)

Steel catenaries are a promising environment for testing of an opticfiber DAS, because fatigue monitoring is of critical importance in atleast two zones. At the upper end of the riser, the complex loadingconditions result in a need for detailed knowledge concerning the hangoff angle and its variation in time. This will be particularlybeneficial in the region of the touch down point, where there is acontinuously varying riser angle which is not straightforward toevaluate using discrete sensors. The central portion of the watercolumn, where the riser angle varies only slightly with depth, is aregion that has not been widely observed with conventional monitoringtechnology. The application of an optic fiber DAS in accordance withembodiments of the invention will allow operators to have detailedinformation concerning the mode shapes along the entire length of theserisers, as well as their relative amplitudes.

Top Tensioned Riser (TTR)

For a TTR, interface loads at the seabed and at the hull riser guidelocations need monitoring. Usefully, the distributed monitoring systemcan provide information concerning riser tensioner stroke, fatiguecycles at the stress joints, and vortex induced vibration (VIV)information. The VIV monitoring would be performed in much the samemanner as for SCRs.

Flexible Riser

Flexible risers offer an opportunity to capitalize on the key strengthsfor the acoustic positioning optic fiber DAS technology. Flexible risersfacilitate greater vessel motion than the other risers described so far.In the case where multiple flexible risers emanate from a single vessel,the risers can be at risk of entanglement. Acoustic positioning can beuseful for monitoring these situations in real time. Since flexible pipeexhibits very little bending stiffness, ocean currents can inducegreater lateral motion than in the case of TTRs or SCRs. In the regionswhere flexible risers are forced to exhibit high bending radii, fatiguecycles are important to monitor. An optic fiber DAS of the presentembodiments would be well suited to monitoring these types of risers,particularly where the fiber installation can be controlled at the timeof the original riser deployment to ensure maximum riser/fiber cohesion.

Drilling Riser

Drilling risers are potentially a very good application for themonitoring technology of the described embodiments. The predictablegeometry and potential proximity of the optical cable to the riserexterior are ideal for the acoustic positioning system capability.Further, the need for detailed VIV information during drilling meansthat the information generated by the system returns data which is ofhigh value to the end user.

Hybrid Riser

Hybrid risers offer a geometry which is a combination of drilling andflexible risers. The capabilities from these two types of systems(above) can be combined in a hybrid installation. Thus the capabilitiesof the optic fiber DAS-based systems of the above described embodimentscan be customized to ensure maximum value in both the flexible uppersection and the stiff vertical section.

Installation Effects

As discussed above, there exists within subsea operations a variety oftypes of risers on which optic fiber DAS-based monitoring can besuccessfully implemented. In those cases where it is not possible toinstall a new fiber (e.g. n those cases where it is desired to retrofitthe interferometer and processor to the end of an existing opticalfiber), the installation of the pre-existing cable will affect the wayin which the system operates. Two of the key issues affectingtransduction, being cable insulation and cable clamping, are presentedbelow.

It was mentioned earlier that cable insulation is an important factor indetermining the acoustic sensitivity of a given cable. Insulation ishowever neither universally beneficial nor detrimental to cablesensitivity. In designing specialty acoustic transduction cables, somelightweight cable coatings can be helpful in reducing the impedancemismatch between a cable and its surroundings. This mechanical matchingcan allow some armored cables to exhibit unexpectedly high acousticsensitivity. Generally, however, armored fiber optic cables which havenot been specially designed with acoustic observation in mind aremediocre performers from an acoustic transduction standpoint. Anadditional type of ‘insulation’ arises from materials standing betweenthe cable and the medium of interest. Consider for instance an umbilicalcontained within the cross-section of a riser. That umbilical will beacoustically obscured from the surroundings rendering it difficult toperform effective acoustic transduction. Therefore in order to maximizethe signal-to-noise ratio for the acoustic positioning embodimentsabove, it is best to take advantage of cables which are in directcontact with the surroundings and specialized for acoustic observation.

With respect to effects arising from clamps, many risers feature cableswhich are clamped to the riser. These clamps can be present in a varietyof forms, each of which will affect transduction. Since the acousticenergy of interest in the acoustic positioning embodiments is on theorder of 10 s of kilohertz and clamps are most generally made of densemetals at spacings on the order of 10 s of meters, the clamps are notacoustically relevant. However, the vortex-induced-vibrations ofinterest for the vibration detection embodiments are at very lowfrequencies, and therefore consist of waves long enough to encompassmany (or even many 10 s of) clamps. These clamps are therefore relevantto the vibration detection embodiments.

Three main classes of clamps exist; continual clamps, where a line iscontained within a groove; interior clamps, where spacers suspend theline within the riser cross-section; and exterior clamps, where the lineis suspended outside the cross-section of the riser using clamps. Forvibration monitoring, where the waves of interest are 100 m long orlonger, the inter-clamp spacing is unimportant provided that the clampstructure is rigid and semi-regular. This is because the clamps arerigid from the perspective of waves much below 50 Hz, and they willtherefore convey all of the information of interest. This is independentof whether the cable is suspended on the inside or the outside of theriser.

Various modifications, whether by way of addition, deletion orsubstitution may be made to the above described embodiment to providefurther embodiments, any and all of which are intended to be encompassedby the appended claims.

REFERENCES

-   Fistas, N., & Manikas, A. (1994). A new general global array    calibration method. ICASSP Proceedings (pp. 73-76). IEEE.-   Kamil, Y. (2011). Localisation and tracking in arrayed wireless    sensor networks. London: Theis (PhD), Department of Electrical and    Electronic Engineering, Imperial College London.-   Knudsen, V. O., Alford, R. S., & Emling, J. W. (1948). Underwater    ambient noise. Journal of Marine Research (7), 410.-   Kutlik, R., & Allen, J. (1998). Flow Assurance Instrumentation.    Offshore Technology Conference, 8733-MS.-   Mellen, R. H. (1952), Thermal-noise limit in the detection of    underwater acoustic signals. Journal of the Acoustical Society of    America, 24, 478.-   Thorp, W. H. (1966). Analytic Description of the low frequency sound    attenuation in the Deep Ocean. Journal of the Acoustical Society of    America, 39 (904).-   Urick, R. J. (1984). Ambient noise in the sea. Department of the    Navy (US), Naval Sea Systems Command. 20070117128.-   Urick, R. J. (1967). Principles of underwater sound (Vol. 3). Los    Altos, Calif., USA: Peninsula Publishing.-   Urick, R. (1983). Principles of underwater sound. McGraw-Hill.

The invention claimed is:
 1. A method of monitoring a shape of a subseariser, comprising: deploying a plurality of acoustic sources at knownpositions in an area in which the subsea riser to be monitored islocated; deploying an optical fiber distributed acoustic sensor on thesubsea riser, the subsea riser being tethered between two points andfree to change shape between the two points, and the optical fiberdistributed acoustic sensor comprising a sensing optical fiber thatextends along the subsea riser and is affixed to the subsea riser in aknown relationship with respect to the subsea riser such that it isknown which part of the optical fiber is adjacent and connected to whichpart of the subsea riser; emitting positioning acoustic signals from theplurality of acoustic sources; using the optical fiber distributedacoustic sensor to detect, at a plurality of acoustic sensor positionsalong the sensing optical fiber, the positioning acoustic signalsemitted by the plurality of acoustic sources; calculating relativepositions of a plurality of the acoustic sensors in dependence on thedetected acoustic signals from the acoustic sources; and from thecalculated positions of the sensors along the fiber, determining a shapeof the subsea riser in dependence on the known relationship between thefiber and the subsea riser.
 2. A method according to claim 1, whereinthe relative position of one of the acoustic sensors on the fiber isdetermined in dependence upon the relative position determined for oneor more others of the sensors.
 3. A method according to claim 2, whereinthe relative position found for one of the acoustic sensors on the fiberis checked to determine whether it is within an allowable distance ofthe position previously found for another of the acoustic sensors on thefiber, given the known length of fiber between the respective positionsof the two acoustic sensors on the fiber.
 4. A method according to claim1, wherein the relative position of one of the sensors is determined independence on the time taken for respective signals from one or more ofthe acoustic sources of known position to reach the sensor.
 5. A methodaccording to claim 1, wherein the calculating further comprises: forminga plurality of subsets of the acoustic sensors, a subset of sensorscomprising a virtual line array of acoustic sensors, and determiningdirection from a subset of sensors to an acoustic source of knownposition in dependence on a phase delay of receipt of an acoustic signalfrom the acoustic source across the acoustic sensors of the array.
 6. Amethod according to claim 5, wherein the subsets of sensors overlap,such that any one acoustic sensor is a member of more than one subset.7. A method according to claim 5, wherein the position of a subset isdetermined by detecting direction to n acoustic sources, where there aren degrees of freedom of the sensors forming the subset.
 8. A methodaccording to claim 1, and further comprising: detecting backscatteredlight on the fiber, the backscatter being dependent on strain induced inthe fiber due to mechanical strain in the subsea riser to which thefiber relates caused by vibrations in the subsea riser; from thedetected backscatter, processing a signal representative thereof todetermine a frequency of oscillation of the vibrations in the subseariser.
 9. A method according to claim 8, and further comprisingfrequency filtering the signal detected by the optical fiber distributedacoustic sensor into low frequencies and high frequencies, wherein thelow frequencies (<100 Hz) are used for vibration detection, and the highfrequencies (>1 kHz) are used for position monitoring.
 10. A methodaccording to claim 1, and further comprising undertaking passiveacoustic monitoring.
 11. A method according to claim 10, wherein thepassive acoustic monitoring comprises detecting acoustic events havingan energy greater than a predetermined energy threshold.
 12. A methodaccording to claim 1, and further comprising repeatedly determining theshape, or shape and position, of the subsea riser so as to track changesin shape and/or movement of the subsea riser with respect to time.
 13. Amethod according to claim 12, and further comprising undertaking fatiguemonitoring or analysis of the subsea riser in dependence on the trackedchanges in shape and/or movement of the subsea riser.
 14. A methodaccording to claim 13, further comprising outputting an alarm based onthe fatigue monitoring or analysis of the subsea riser.
 15. A methodaccording to claim 1, wherein the optical fiber is clamped to the subseariser.
 16. A system for monitoring a shape of a subsea riser,comprising: a plurality of acoustic sources at known positions in anarea in which the subsea riser to be monitored is located; an opticalfiber distributed acoustic sensor deployed on the subsea riser, thesubsea riser being tethered between two points and free to change shapebetween the two points, and the optical fiber distributed acousticsensor comprising a sensing optical fiber that extends along the subseariser and is affixed to the subsea riser in a known relationship withrespect to the subsea riser such that it is known which part of theoptical fiber is adjacent and connected to which part of the subseariser; and a processor arranged to receive acoustic data from theoptical fiber distributed acoustic sensor representative of detectedacoustic signals detected by the optical fiber distributed acousticsensor, wherein in use: a) the optical fiber distributed acoustic sensordetects, at a plurality of acoustic sensor positions along the fiber,acoustic signals emitted by the plurality of acoustic sources; and b)the processor: i. calculates relative positions of a plurality of theacoustic sensors in dependence on the acoustic data representative ofthe detected acoustic signals from the acoustic sources; and ii. fromthe calculated positions of the sensors along the fiber, determines ashape of the subsea riser in dependence on the known relationshipbetween the fiber and the subsea riser.
 17. A system according to claim16, wherein the relative position of one of the acoustic sensors on thefiber is determined in dependence upon the relative position determinedfor one or more others of the sensors.
 18. A system according to claim17, wherein the relative position found for one of the acoustic sensorson the fiber is checked to determine whether it is within an allowabledistance of the position previously found for another of the acousticsensors on the fiber, given the known length of fiber between therespective positions of the two acoustic sensors on the fiber.
 19. Asystem according to claim 16, wherein the relative position of one ofthe sensors is determined in dependence on the time taken for respectivesignals from one or more of the acoustic sources of known position toreach the sensor.
 20. A system according to claim 16, wherein thecalculating further comprises: forming a plurality of subsets of theacoustic sensors, a subset of sensors comprising a virtual line array ofacoustic sensors, and determining direction from a subset of sensors toan acoustic source of known position in dependence on a phase delay ofreceipt of an acoustic signal from the acoustic source across theacoustic sensors of the array.
 21. A system according to claim 16,wherein the optical fiber distributed acoustic sensor further comprises:an interferometer arrangement arranged to detect backscattered light onthe fiber, the backscatter being dependent on strain induced in thefiber due to mechanical strain in the subsea riser to which the fiberrelates caused by vibrations in the subsea riser, wherein the processoris further arranged, from the detected backscatter, to process a signalrepresentative thereof to determine a frequency of oscillation of thevibrations in the subsea riser.
 22. A system according to claim 16, andfurther comprising one or more clamps arranged to affix the opticalfiber to the subsea riser.